Equations comparison

The intermediate length (tube diameter) 2 can be estimated from the modulus with the aid of the above equations. Comparison of values of the intermediate length found from dynamic modulus and from neutron-scattering experiments was presented by Ewen and Richter (1995). They found the values to be close to each other, though there is a difference in the temperature dependence of the values of intermediate length found by different methods. 

Rate equation, comparisons, 30 Rate theory, 3, 28-38 Ratiograms, 83, 86 Recycle, 226... 

Davis, M. E. and J. A. McCammon. (1989). Solving the finite difference linear Poisson Boltzmann equation Comparison of relaxational and conjugate gradient methods. J Comp. Chem. 10 386. 

Arrhenius parameters for the dehydrations of ammonium and potassium aliuninium alums [38] were in agreement with the Polanyi-Wigner equation. Comparisons of the shapes of nuclei on different crystal surfaces indicated that reaction proceeds along (100) planes. The observed decrease of the rate in water vapour is attributed to the blocking of pores by adsorbed molecules. No intranuclear cracking was apparent and the product-reactant boimdaries became irregular because of the influence of water on reorganization of the product phase. The appearance of these nuclei contrasted markedly with those in mixed potassium chromium/aluminium alums, where there is an approximately concentric structure. 

Concentration profiles of titanium(IV) species in the feed, carrier, and strip solutions were calculated using model equations. Comparison of the experimental and the simulated data shows that ... 

Table 18.8 Intermediate pressures after 100 s found by applying the Method of Referred Derivatives to the full flow equations and to the modified flow equations. Comparison with exact values...

The solution of the problem in the present approximation is the sum of (13) and (14 b). Had we used the diffusion equation right from the start, the solution would have been only the last term of (14 b). One sees that the present procedure gives a much more nearly correct result at small distances. In particular, the density is l/Airr v near the origin, as it is in the accurate solution. However, at large distances the behavior of the sum of (13) and (14 b) is the same as that of the solution of the diffusion equation. Comparison with (10) shows that it is too large by the factor 1/J. Neither will this behavior change... 

Thus, any substrate that can add last can bind either in rapid equilibrium or in steady-state fashion without changing the form of the rate equation. Comparison of Eqs. (8.2) and (8.7), however, shows that a substrate that cannot add last will change Ae rate equation if it adds in rapid equilibrium. 

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